Immunological-based approach for accurate fitting of 3D noisy data points with Bézier surfaces

Free-form parametric surfaces are common tools nowadays in many applied fields, such as Computer-Aided Design & Manufacturing (CAD/CAM), virtual reality, medical imaging, and many others. A typical problem in this setting is to fit surfaces to 3D noisy data points obtained through either laser scanning or other digitizing methods, so that the real data from a physical object are transformed back into a fully usable digital model. In this context, the present paper describes an immunologicalbased approach to perform this process accurately by using the classical free-form Bézier surfaces. Our method applies a powerful bio-inspired paradigm called Artificial Immune Systems (AIS), which is receiving increasing attention from the scientific community during the last few years because of its appealing computational features. The AIS can be understood as a computational methodology based upon metaphors of the biological immune system of humans and other mammals. As such, there is not one but several AIS algorithms. In this chapter we focus on the clonal selection algorithm (CSA), which explicitly takes into account the affinity maturation of the immune response. The paper describes how the CSA algorithm can be effectively applied to the accurate fitting of 3D noisy data points with Bézier surfaces. To this aim, the problem to be solved as well as the main steps of our solving method are described in detail. Some simple yet illustrative examples show the good performance of our approach. Our method is conceptually simple to understand, easy to implement, and very general, since no assumption is made on the set of data points or on the underlying function beyond its continuity. As a consequence, it can be successfully applied even under challenging situations, such as the absence of any kind of information regarding the underlying function of data

Reconstrucción de curvas B-spline y de Bézier mediante selección clonal

Máster en Matemáticas y Computació

Técnicas metaheurísticas de base immnunológica para la reconstrucción de curvas y superficies de forma libre

ABSTRACT: This PhD thesis is focused on the application of a powerful metaheuristics belonging to the family of the artificial immune systems and called clonal selection algorithm (ClonalG) to solve the free-form curve and surface reconstruction problem with both local-support and global-support functions from clouds of noisy data points. Our methodology has been applied to solve this problem in several relevant cases, such as polynomial and rational Bézier and B-spline curves and surfaces in both the parametric and the explicit cases. Our methods can be applied to sets of data points subjected to noise, irregular sampling and other artifacts typically found in real-world applications. Other relevant contribution is the hybridization of the ClonalG algorithm with local search techniques to enhance the efficiency of the optimization process. This thesis work has led to several publications in relevant JCR-indexed journals (Q1 and Q2) as well as in prestigious international conferences in the field.RESUMEN: Esta tesis se centra en la aplicación del algoritmo de selección clonal, ClonalG (una potente metaheurística englobada dentro de los llamados sistemas immunitarios artificiales), para resolver el problema de la reconstrucción de curvas y superficies de forma libre mediante funciones de soporte global y de soporte local a partir de nubes de puntos dato ruidosos. La metodología ha sido aplicada a resolver este problema en los casos relevantes de curvas y superficies de Bézier y B-splines, tanto polinomiales como racionales, y tanto en su versión paramétrica como explícita. Nuestros métodos pueden ser aplicados a nubes de puntos dato afectados por ruido, muestreado irregular y otros problemas típicos en aplicaciones del mundo real. Otra contribución relevante es la hibridación del algoritmo ClonalG con otras técnicas de búsqueda local para mejorar la eficiencia de la optimización. La tesis viene avalada por un buen número de publicaciones en revistas relevantes (Q1 y Q2) del JCR, así como en congresos internacionales de referencia en su campo.The work presented in this thesis has been financially supported by two research projects from the National Program of Research, Development and Innovation: • the project from the National Program of Computer Science entitled “Artificial Intelligence for Geometric Modeling and Computer Graphics” (Ref. TIN2006-13615), of the Direcci´on General de Investigaci´on of the Spanish Ministry of Science and Education. • the project from the National Program of Computer Science entitled “Metaheuristics for Automatic Reconstruction of Free-Form Curves and Surfaces for Reverse Engineering” (Ref. TIN2012-30768), of the Direcci ´on General de Investigaci´on of the Spanish Ministry of Economy and Competitiveness